Parallel Submanifolds of Symmetric Spaces

Resumen:

Among the fundamental objects attached to a submanifold M of a Riemannian manifold N is its so-called second fundamental form.

For example the totally geodesic submanifolds are characterized by the vanishing of their second fundamental form.

Generalizing the concept of totally geodesic submanifolds I will consider the concept of a parallel submanifold:

A parallel submanifold is a submanifold whose second fundamental form is parallel with respect to a natural connection.

Beautiful examples of parallel submanifolds of symmetric spaces are the so called symmetric submanifolds, for example the round Cylinder 

in the three dimensional Euclidean space. It turns out that every parallel submanifold of a Euclidean space shares this property. 

At the end of my talk I will present my classification of parallel submanifolds of a real 2-Grassmannian.

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